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How to calculate the shortest effective cutting length of gear hob

the shortest effective cutting length of the gear hob refers to the shortest axial length (l0t) min of the hob required to cut out the full tooth height of the gear. In gear machining, there are many cases that need to calculate the shortest effective cutting length of hob. For example, when hobbing the pinion of the duplex gear, if the pinion is a helical gear and is very close to the big gear, it is necessary to check whether the hob will collide with the big gear when hobbing the pinion. The smaller the outer diameter of the hob and the shorter the axial length, the less likely it is to collide with the big gear. However, if the outer diameter of the hob is too small, the strength of the keyway part of the tooth root will be affected (at this time, it can be considered to make the hob and the cutter shaft into one); In addition, if the axial length of the hob is too short, the complete pinion may not be cut out. Therefore, in this case, it is necessary to calculate the shortest axial length of the hob. In addition, (l0t) min is also the basis for calculating the total length of hob teeth (considering the length of tool string)

1 calculation method

can deduce and calculate the (l0t) min when hobbing spur gears. For ordinary precision hobs, because the spiral rise angle is very small, it can be considered that the normal tooth shape angle is equal to the axial tooth shape angle. Let the intersection of the meshing line of the tangent point P and the diameter of the gear addendum circle be a, and the intersection with the hob addendum line be B, then the tooth shape of the workpiece is formed between the meshing line a and B. The vertical line of the meshing line passing through point a intersects with the top line of the hob tooth at C '. Let the top tooth angle of the hob outside C' be C, then the shortest distance along the normal direction of the hob tooth part (that is, the shortest length of cutting the full tooth height of the gear without tool string) is (l0n) min=2 (pm/2+ce) =pm+2l3 (1)

the reason why half of the normal tooth distance of the hob (pm/2) is substituted in the calculation is that it is assumed that the top tooth height of the hob is equal to its tooth root height. Although in fact, it is not required that the hob tooth is difficult to adjust and control, and the top height must be equal to its tooth root height, as long as the full height of the hob tooth is greater than the full height of the workpiece tooth, and the top height of the hob tooth is equal to the tooth root height of the workpiece (the tooth root height of the workpiece is (fa1+c1) m, where FA1 is the tooth top height coefficient of the workpiece, C1 is the radial clearance coefficient, and the tooth root position is shown in RS in Figure 1), it is troublesome to substitute the tooth root height of the workpiece RS for calculation. In order to simplify the calculation, it may be assumed that the hob tooth root height is equal to the hob tooth top height, at this time rs=pm/2. Since the actual hob tooth root height is usually less than the workpiece tooth root height, the hob (l0n) min value calculated according to formula (1) increases slightly, and the calculation result is safer

it can be seen that in order to cut the complete tooth profile of the hob, L3 ≥ L2 must be met. Because the shortest length of the hob needs to be calculated, its limit case l3=l2 can be taken. L2 is the length actually involved in cutting. This length is taken when machining duplex gears for checking calculation. Its calculation formula is L2 =l1+qa=l1+qc'tana1 =l1+en tana1=l1+ (np+me-pm) tana1

= l1+[l1tana1+ (fa1+c1) m-x1m]tana1

= (tan2a1+1) l1+ (fa1+c1-x1) mtana1

(2) where: l1=ra1sin (aa1-a1) ra1.1. The radius of the addendum circle of the workpiece Aa1. The pressure angle of the addendum circle of the workpiece, cosaa1=rb1/ra1=mz1cosaa1/ra1. After L2 is obtained, If L3 ≥ L2 is taken, then (l0n) min can be obtained by substituting into equation (1), and the shortest axial length of the hob is (l0t) min= (l0n) min/cosg0

(3). In the equation, the spiral rise angle of G0 hob is usually small (about 3 °, cos3 ° ≈ 0.9986), and the shortest effective cutting length of the hob is rounded to mm at the end, so (l0n) min can also be directly taken as (l0t) min

although the above formula is derived from the case of hobbing straight cylindrical gears, if the relevant parameters are changed into normal parameters and the equivalent gear is used to replace the workpiece, it can also be approximately used in the calculation of helical cylindrical gears. If it is necessary to check whether the pinion will collide with the big gear when hobbing the duplex gear, take twice the L2 calculated by formula (2) as (l29.420t) min, That is, (l0t) min=2l2 is the "anjianneng classic extreme series and anjianneng classic optimization series" involved in cutting, which shows our commitment to deliver customer value innovation in the field of thermal insulation materials. The shortest length of the hob is calculated by formula (1) and is the shortest length that the hob should have without tool string.

2 application examples

example 1: the parameters of the gear workpiece in our factory are: da1=96.2mm, diameter pitch p=8 (i.e. m=3.175mm) , z1=29, a1=20 °, tooth full height h 1=5.733mm, tooth tip height h a1=2.0. In this sense, the function of using pulse fatigue testing machine is to reduce similar events by 6mm. The outer diameter is 90mm, and the diameter of the dividing circle d0=82 The gear is hobbed with a 654mm single head hob, and the shortest length of the tooth part of the hob is calculated. Solution: first, calculate the pressure angle Aa1 of workpiece addendum circle: cosaa1=mz1cosaa1/ra1=0

aa1=25.9208 ° l1=ra1sin (aa1-a1) =4.96mm workpiece tooth root height coefficient is fa1+c1= (h1-ha1)/m=1.15l2= (tan2a1+1) l1+ (fa1+c1-x1) mtana1=6.94mm because l3>l2, l3=7 is taken. Then the shortest normal length of the hob is (l0n) min=pm+2l3 ≈ 24mm. The hob is a single head, and its spiral rise angle is g0=arcsin (m/d0) =2 Then (l0t) min= (l0n) min/cosg0=24.01mm

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